Screening of dust grains in a weakly ionized gas: Effects of charging by plasma currents

Screening and charging of a grain in a weakly ionized plasma background are studied within the drift-diffusion approximation. The computations evidence that the account of grain charging results in a distinct qualitative change in the screened field as compared to the thermodynamically equilibrium case of a grain with a constant charge. The stationary grain charge as well as the field within the sheath around the grain are shown to be almost independent of the type of boundary conditions (for relatively low ionization rates and small grain sizes), whereas the asymptotical behavior of the effective field is rather sensitive to them.